SKI 037-2 Version 21bsgmodifications separateappendix-fina.

SKI Perspective

Background

The travel times of radionuclides from a spent nuclear fuel repository to the surfaceenvironment is mainly determined by the direction and magnitude of groundwater flow aswell as chemical reactions of nuclides on solid surfaces. The travel time for a specific nuclidecan be regarded as an important characteristic in the overall evaluation of the long-term safetyfor such repositories. Radionuclides can move with the groundwater either as solutes orcolloids (minute particles in the range 1nm to 1 µm), where the latter mechanism generallyresults in much shorter travel times for radionuclides that interact strongly with solid phases,such as actinides. In performance assessment is it therefore essential to assess the relativeimportance of these two transport mechanisms for different nuclides. The relative importanceof colloids depends on the nature and concentration of colloids in groundwater.

Galson Sciences has previously completed a study for SKI in which international experiencesrelated to the treatment of colloid transport in performance assessment calculations issummarised (SKI Report 00:33). This study complements the previous one by including aquantitative evaluation of the significance of plutonium transport with colloids for conditionsrepresentative of deep Swedish groundwaters. Plutonium was chosen as an example of arelevant nuclide because new information was available about its behaviour in groundwaterfrom the Nevada test site.

Relevance for SKI

SKI need to develop, maintain and update independent modelling capability in order toachieve a detailed understanding of different phenomena of relevance for the long-term safetyof spent fuel and other nuclear waste and to evaluate key conclusions from previouslypublished safety assessments. This study contributes to the achievement of that goal by testingand implementing the previously developed COLLAGE II code, which considers radionuclidetransport as solutes as well as on colloids.

Results

The modelling results show that transport of plutonium by colloids can not be ruled out as asignificant transport pathway relative to the solute transport pathway, based on the availableinformation about sorption/desorption kinetics, colloid concentrations, sorption strength, etc.The study also includes a sensitivity analysis that especially contributes to an understandingof the significance of sorption kinetics in the context of colloid transport.

Future work

The present version of the COLLAGE II code can be improved by adding a more detailedmodel for sorption and desorption reactions and a more realistic representation of the releaseof nuclides at the inner boundary. It would also be possible to analyse other nuclides apartfrom plutonium, but additional experimental/field data would then be needed.

Project information

SKI project manager: Bo Strömberg

Project identification number: 00183

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Summary

Colloids are minute particles in the size range 1 nm to 1 µm that can remainsuspended in water, and may influence radionuclide transport in radioactive wastedisposal systems. Galson Sciences Ltd (GSL) has undertaken a quantitativeassessment of the impact that colloid-facilitated radionuclide transport may have onthe performance of the Swedish KBS-3 concept for disposal of high-level radioactivewaste and spent fuel. This assessment has involved the evaluation and application ofSKI’s colloid transport model, COLLAGE II, modelling of km-scale Pu transport atthe Nevada Test Site (NTS), USA, and identification of circumstances under whichcolloid-facilitated transport could be important for a KBS-3-type environment.

Colloids bearing traces of plutonium from the BENHAM underground nuclear testhave been detected in samples obtained from Nevada Test Site (NTS) groundwaterwells 1.3 km from the detonation point. Plutonium is generally fairly immobile ingroundwater systems, and it has been suggested that colloids may have caused theplutonium from the BENHAM test to be transported 1.3 km in only 30 years. Thishypothesis has been tested by modelling plutonium transport in a fracture with similarcharacteristics to those present in the vicinity of the BENHAM test.

SKI’s colloid transport code, COLLAGE II, considers radionuclide transport in a one-dimensional planar fracture and represents radionuclide-colloid sorption anddesorption assuming first-order, linear kinetics. Recently published data from both theongoing NTS site investigation and from the associated Yucca Mountain Project havebeen used to define a COLLAGE II dataset. The kinetics of radionuclide-colloidsorption and desorption have been found to be crucial in explaining the transport ofplutonium associated with colloids, as inferred at the NTS. Specifically, it has beenfound that for plutonium to have been transported by colloids over the full 1.3 kmtransport path, it is likely that the plutonium was released in colloidal form and thatthe rate of plutonium desorption from colloids must have been slow.

For the KBS-3 situation, the Aberg fracture from the SR97 performance assessmenthas been used to provide the basis for a COLLAGE II representation of colloidtransport. Colloid concentrations of typical Swedish groundwaters have been used,together with literature information on the strength of radionuclide-colloid sorption.

Modelling results indicate that colloids may play a role in contaminant transport ifradionuclides sorb strongly, and irreversibly or nearly irreversibly, to colloids.Furthermore, if the rates of radionuclide sorption and desorption to colloids lie in acertain range, then there exists the possibility that colloid-facilitated transport couldlead to relatively rapid (<100 year) transport of radionuclides from the bentonite-hostrock interface to the accessible environment. Early release will only occur over arelatively restricted range of low sorption/desorption rates. At these low rates, even ifall plutonium is initially released to far-field groundwaters in solution, followingdiffusion through the bentonite buffer, a small amount is able to associate withgroundwater colloids. Because of the slow rate of disassociation, this plutonium isthen able to be carried significant distances on colloids before being released to

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solution where it is rapidly sorbed onto mineral surfaces. Were the strength ofsorption of plutonium to colloids, or the concentration of colloids, to be greater thancurrent best estimates, there could be a relatively greater early release.

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Sammanfattning

Kolloider är små partiklar i storleksordningen 1 nm till 1 µm som kan förbli svävandei vatten, och som kan påverka radionuklidtransporten från ett slutförvar medradioaktivt avfall. Galson Sciences Ltd (GLS) har genomfört en kvantitativ studie avvilken betydelse kolloidal radionuklidtransport kan ha för funktionen av ett svensktKBS-3 förvar med använt kärnbränsle. Denna studie innehåller en utvärdering ochtillämpning av SKI:s kolloidtransportmodell (COLLAGE II), modellering av plutoniumtransport (i km-skala) vid Nevada Test Site i USA, och identifiering av förhållandenunder vilka kolloidtransport skulle kunna vara betydelsefull för ett KBS-3 förvar.

Kolloider med spår av plutonium från BENHAM "underground nuclear test" hardetekterats i prov tagna från Nevada Test Sites grundvattenbrunnar belägna 1.3 kmfrån detoneringspunkten. Plutonium är vanligtvis relativt immobilt i grundvattensystem,och man tror att kolloider kan vara orsaken till att plutonium från BENHAM testet hartransporterats 1.3 km på bara 30 år. Denna hypotes har testats genom modellering avplutoniumtransport i en spricka med liknande egenskaper som de i omgivningen avBENHAM testet.

SKI:s kolloidtransportkod, COLLAGE II, beskriver radionuklidtransport i enendimensionell, plan spricka och representerar radionuklid-kolloid sorption/desorptiongenom att antaga en första-ordningens linjär kinetik. Nyligen publicerade data, både frånde pågående platsundersökningarna vid NTS och från Yucca Mountain projektet, haranvänts för att definiera ett dataset för COLLAGE II. Radionuklid/kolloid sorptions-desorptionskinetiken har visat sig vara avgörande i förklaringen till transporten av plutoniummed kolloider. Mer specifikt har det visat sig att det plutonium som har transporteratsav kolloider hela den 1.3 km långa transportvägen troligen släpptes ut i kolloidal form ochatt hastigheten för plutonium desorptionen i detta fall måste ha varit långsam.

För KBS-3 fallet har data för A-berg (Äspö) från säkerhetsanalysen SR 97 använts sombas för en COLLAGE II representation av kolloidtransport. Kolloidkoncentrationer hostypiska svenska grundvatten har använts tillsammans med litteraturdata om styrkan påradionuklid-kolloid sorption.

Modellresultat visar att kolloider kan ha betydelse för radionuklidtransporten omradionukliderna sorberar starkt och irreversibelt eller nästan irreversibelt till kolloiderna.Om dessutom hastigheten av radionuklidenas sorption/desorption till kolloider liggerinom ett visst intervall så är det möjligt att kolloidtransporten kan leda till en relativtsnabb (mindre än 100 år) radionuklidtransport från bentonit-berg-gränsytan till dentillgängliga miljön. Ett tidigt utsläpp sker endast över ett relativt begränsat intervall avlåga sorptions/ desorptions-hastigheter. Vid dessa låga hastigheter kan små mängderplutonium bindas till kolloider i grundvattnet, även om allt tillgängligt plutonium initialtsläpps ut i grundvatten i närheten av förvaret efter att ha passerat bentonitbufferten viadiffusion. På grund av den långsamma dissociationshastigheten så kan detta plutoniumbäras långa avstånd på kolloiderna innan de desorberar och släpps ut igen i grundvattnetdär de sedan snabbt sorberar på mineralytor. Om sorptionsstyrkan av plutonium tillkolloider, eller kolloidkoncentrationen, vore större än de nuvarande bäst uppskattadevärdena, skulle ett relativt större utsläpp i ett tidigt skede kunna förekomma.

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Contents

1 Introduction ..........................................................................................................1

1.1 Background and Objectives ............................................................................... 11.2 Report Structure ................................................................................................. 2

2 Overview of the COLLAGE II Model for Colloid-FacilitatedTransport ..............................................................................................................3

2.1 Background ........................................................................................................ 32.2 Conceptual Model.............................................................................................. 32.3 Mathematical Model .......................................................................................... 42.4 COLLAGE II Parameterisation ......................................................................... 7

3 Modelling NTS Conditions with COLLAGE II.................................................9

3.1 Background ........................................................................................................ 93.2 Database............................................................................................................. 9

3.2.1 Fracture and Groundwater ......................................................................... 93.2.2 Colloids .................................................................................................... 10

3.3 Results.............................................................................................................. 153.4 Discussion ........................................................................................................ 18

4 The Potential Influence of Colloids in Swedish PAs .......................................22

4.1 Background ...................................................................................................... 224.2 Colloid Transport in the KBS-3 Concept......................................................... 22

4.2.1 Model Parameterisation ........................................................................... 224.2.2 Model Results and Discussion ................................................................. 27

4.3 Probabilistic Sensitivity Analysis .................................................................... 314.3.1 Model Parameterisation ........................................................................... 314.3.2 Model Results and Discussion ................................................................. 314.3.3 Key Parameter Sets .................................................................................. 37

4.4 Other Radionuclides......................................................................................... 40

5 Conclusions .........................................................................................................41

5.1 Modelling Plutonium Transport at the Nevada Test Site................................. 415.2 Colloids in Swedish PA ................................................................................... 42

References...................................................................................................................44

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List of Figures

Figure 2.1: Illustration of the COLLAGE II conceptual model for colloid transportin a thin planar fracture. .............................................................................. 4

Figure 3.1: Kinetics of plutonium - groundwater interactions. ................................... 14

Figure 3.2: Plutonium transport in the NTS reference fracture for a variety ofconditions. ................................................................................................. 16

Figure 3.3: Influence of radionuclide-colloid sorption/desorption rate onradionuclide release flux (solute + colloid) at the NTS. Case of allradionuclide release on colloids. ............................................................... 19

Figure 3.4: Influence of radionuclide-colloid sorption/desorption rate onradionuclide release flux (solute + colloid) at the NTS. Case of allradionuclide release in solution................................................................. 19

Figure 3.5: COLLAGE II output for artificially increased values of thepartitioning coefficient k1.......................................................................... 20

Figure 4.1: Results for the KBS-3 reference case. ...................................................... 29

Figure 4.2: Effect of low values of the sorption/desorption rate, κ1, on plutoniumbreakthrough curve. .................................................................................. 29

Figure 4.3: Effect of sorption - desorption rate (κ1) on the colloid-born release at12.6 years for the KBS-3 dataset. ............................................................. 30

Figure 4.4: Scatter plots of key parameters showing their influence on peak totalrelease flux. ............................................................................................... 34

Figure 4.5: Scatter plots of time of peak release vs. radionuclide - colloid sorptioncoefficient, Kp. .......................................................................................... 35

Figure 4.6: Scatter plots of time of peak release vs. sorption/desorption rate, κ1. ...... 35

Figure 4.7: Colloid and solute fluxes from sample run 30 compared to the casewith no colloids......................................................................................... 38

Figure 4.8: Identification of pessimistic case colloid transport parameters forgroundwater conditions and colloid populations defined by Swedishsaline and non-saline groundwaters. ......................................................... 38

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List of Tables

Table 2.1: Parameters in the COLLAGE II code. ........................................................ 5

Table 3.1: Reference dataset for the representation of the BENHAM fracture. ........ 11

Table 3.2: Colloid load in NTS groundwaters. .......................................................... 12

Table 3.3: Radionuclide partition coefficient, k1........................................................ 12

Table 3.4: Variations on the NTS reference case dataset........................................... 16

Table 3.5: Summary of NTS simulation test cases investigating the role ofsorption/desorption kinetics and the form of the release to the fracture. .. 17

Table 4.1: Reference dataset for the representation of an Aberg fracture inCOLLAGE II. ........................................................................................... 25

Table 4.2: Values for colloid load (αm) in a variety of fractured granites. ................ 26

Table 4.3: Values of the radionuclide - colloid partition coefficient (k1) for arange of radionuclide - colloid sorption coefficients (Kp) and colloidloads (αm). ................................................................................................. 26

Table 4.4: Variations on the KBS-3 reference case. All release in solution. ............. 28

Table 4.5: List and justification of parameters sampled in the probabilisticsensitivity analysis. ................................................................................... 32

Table 4.6: Analysis of the probabilistic sensitivity analysis of plutoniumtransport in a KBS-3 fracture. ................................................................... 33

Table 4.7: Key parameters characterising plutonium transport in Swedishfractures in the KBS-3 concept. ................................................................ 39

1

Quantitative Assessment of the PotentialSignificance of Colloids to the

KBS-3 Disposal Concept

1 Introduction

1.1 Background and Objectives

Colloids are minute particles in the size range 1 nm to 1 µm that can remainsuspended in water. Groundwaters often contain large populations of natural colloids,and these can interact with pollutants and influence their transport. In radioactivewaste disposal systems, natural colloids and waste- and repository-derived colloidsmay influence radionuclide transport. Since the early 1990s, there has been a growingawareness of the potential importance of colloids, and as greater computing resourcesand more data have become available, PA models have increasingly included colloidsin quantitative analyses of repository safety.

Recent observations made by United States Department of Energy (DOE) researchersat the Nevada Test Site (NTS) have demonstrated migration of Pu 1.3 km from thesite of the BENHAM underground nuclear test; the researchers suggest that themigration may have occurred as a result of the attachment of the Pu to colloids(Kersting et al., 1999).

The primary objective of this project has been to evaluate the potential for colloids totransport radionuclides in environments relevant to the Swedish disposal concept. Inorder to assess the role of colloids in the Swedish KBS-3 disposal concept, a reviewof the mechanisms by which colloids could be introduced into the disposal systemenvironment has been carried out (Wickham et al. 2000). This enabled us to form anunderstanding of which and how many colloids may be present in far-field fracturesunder normal circumstances.

Modelling of colloid-facilitated transport is a matter of representing the transport ofradionuclides in solution and on colloids in a network of fractures in granite. TheSwedish Nuclear Power Inspectorate (SKI) has a model designed for the purpose ofcolloid modelling - COLLAGE II (Grindrod and Cooper, 1993). The observationsfrom the NTS provide an opportunity to test COLLAGE II against independent data,and to assess the level of confidence in the use of COLLAGE II. COLLAGE II mayalso be used to represent fractures in the KBS-3 concept, and to assess the potentialrole of colloids in that system.

In the course of the work it has been possible to use the most recent information fromthe Yucca Mountain Project and the NTS site monitoring programmes from the USA.Colloids are of potential importance in both of these programmes.

2

1.2 Report Structure

Section 2 of this report provides a brief review of the COLLAGE II model. Details ofthe mathematical model represented in COLLAGE II and suggestions arising fromour experience with the code are summerised in a technical note available from SKI.

The application of COLLAGE II to the NTS system is described in Section 3. ThisSection includes a review of newly available data from the NTS and Yucca MountainProject. The ability of COLLAGE II to reproduce the NTS observations isinvestigated and the consequences for colloid modelling discussed.

Section 4 applies the lessons learned to a model of a representative fracture in theKBS-3 concept. The crucial role of the sorption/desorption rate of radionuclides ontocolloidal material is investigated in a deterministic sensitivity study, and a widerprobabilistic sensitivity analysis is used to investigate the range of parameters thatmight give rise to significant colloid-driven effects.

Conclusions from the study are presented in Section 5.

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2 Overview of the COLLAGE II Model for Colloid-Facilitated Transport

2.1 Background

COLLAGE II is SKI’s colloid-facilitated radionuclide transport code. It is the maintool used by SKI for quantitative assessment of the potential impact of colloids in theKBS-3 disposal concept.

The model and its development are documented in a series of SKI reports (Grindrod,1989; Grindrod and Worth, 1990; Grindrod, 1991; Grindrod et al., 1992; Grindrodand Cooper, 1993). COLLAGE II calculates the flux of radionuclides released at theend of a saturated planar fracture surrounded by porous media. The flux in solution,the flux attached to mobile colloids, the total flux (solute and colloid), and time-integrated flux are calculated.

Earlier implementations of the code assumed instantaneous irreversible sorption ontocolloidal material but included representations of both mobile and immobile colloids.The most recent version of the code includes reversible interactions betweenradionuclides in solution and on both forms of colloids. These are modelled via first-order kinetics. This project has highlighted the importance of these mechanisms.

Galson Sciences has implemented some modifications to the original COLLAGE IIcoding. These have had the effect of allowing the user greater flexibility in selectingoutput times and the code can now be run more easily with groups of input files. Aprobabilistic version, interfaced to output from the Sandia Latin Hypercube Sampling(LHS) code (Iman and Shortencarrier, 1984), has also been produced for this project.

2.2 Conceptual Model

Figure 2.1 illustrates the features and processes represented in the conceptual modelfrom which the COLLAGE II code is derived. The characteristics of the model aresummarised below.

Radionuclides in solution travel with the groundwater flow within the fracture butinteract with the rock matrix of the fracture walls. If suspended colloidal material ispresent in the fracture, radionuclides can sorb onto the colloids and desorb back intosolution. Some of the colloids may be captured by the walls of the fracture and somemay be released.

The model permits an evaluation of the response of the system, as illustrated in Figure2.1, to the input of radionuclides at the upstream end of the fracture. The response isgiven in terms of the radionuclide flux at the downstream end, both in solution and onmobile colloids.

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In common with a number of colloid modelling approaches, COLLAGE II uses a one-dimensional approach to characterise the fracture properties, with matrix sorption intothe wall rock perpendicular to the direction of flow. Such descriptions have been usedin many cases (e.g., Nagra, 1994; US DOE, 1998; JNC, 2000). A 1-D approach iscurrently also used in the US YMP programme (Wolfsberg and Reimus, 2000).COLLAGE II differs from contemporary models in its treatment of the kinetics ofradionuclide-colloid interactions (see the review by Wickham et al., 2000).

2.3 Mathematical Model

The following provides an overview of the mathematical model represented inCOLLAGE II. Details of the model’s derivation has been summerised in a technicalnote available from SKI.

The fracture has length L [m] and the aperture half-width is b [m]. The boundarybetween the water in the fracture and the wall rock is at z = 0 m. Within the fracture (0≤ x ≤ L), there are three radionuclide concentrations of interest:

cs mol m-3 radionuclide concentration in solution in fracture flow;

cm mol m-3 radionuclide concentration sorbed to mobile colloids; and

cf mol m-3 radionuclide concentration sorbed to immobile colloids.

Additionally the radionuclide concentration in the rock matrix is used:

cp mol m-3 radionuclide concentration sorbed to the rock matrix.

Table 2.1 summarises the other parameters used in the code.

Direction o fgroundwater

flow

Rock matrix

Mobilecolloids

Fixed colloids

Radionuclides in solution

Radionuclides sorbed onto rock walls

Radionuclidessorbed onto mobile

colloids

Radionuclides sorbed onto fixed

colloids

Colloiddetachment

Colloidattachment

Figure 2.1: Illustration of the COLLAGE II conceptual model for colloid transportin a thin planar fracture.

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Table 2.1: Parameters in the COLLAGE II code.

parameter units Definition

D~ m2 y-1 dispersion coefficient of solute

u~ m y-1 average groundwater velocity in the fracture

D m2 y-1 molecular diffusion coefficient of the solute into the rockmatrix

φ - rock matrix porosity

b m half fracture width

∗D m2 y-1 dispersion coefficient of mobile colloids

∗u m y-1 average mobile colloid flow rate

λ y-1 decay constant

R -rock matrix retardation coefficient - dKR ρ

φφ−+= 1

1 where

Kd is the distribution coefficient for radionuclides sorbingonto the rock matrix

1κ y-1 rate of sorption/desorption, mobile colloids

2κ y-1 rate of sorption/desorption, immobile colloids

β - number of mobile colloids/number of immobile colloids

1k - partition coefficient for radionuclides sorbing onto mobilecolloids

2k - partition coefficient for radionuclides sorbing onto immobilecolloids

η - fraction of injected inventory in solute phase

L m length of fracture modelled

n - scaling factor for zero concentration outer boundarycondition at x = nL

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The advection-dispersion equation representing radionuclide exchange betweensolution and colloids is:

( ) ( ) sms

z

psss ckkccz

c

b

D

x

cu

x

cD

t

c221121

0

2

2~~ κκβκκλφ +−++−

∂∂

+∂∂−

∂∂=

∂∂

=

(1)

for radionuclides in solution, and

( ) ( ) ( ) ( ) smmmmm ckkccx

cu

x

cD

t

c2211212

2

11 κκβκκβλβ +++−+−∂∂−

∂∂=

∂∂+ ∗∗ (2)

for radionuclides on mobile colloids.

The model implements a zero concentration outer boundary condition in the fracture:

( ) ( ) 0,0,, ≥== ttnLctnLc ms (3)

The initial condition at x = 0 is a pulse of radionuclides, with zero concentrationelsewhere in the fracture.

( ) ( ) nLxxcxc ms <<== 0,00,0, (4)

The initial pulse at x = 0 is divided into a fraction η in solution and a fraction (1 - η )on mobile colloids, so that the evolution can be described as:

( ) 0,2

1~~

0

≥=

∂∂−

=

ttbx

cDcu

x

ss δη , and (5)

( ) ( ) 0,2

11

0

≥−=

∂∂−

=

∗∗ ttbx

cDcu

x

mm δη . (6)

In the rock matrix, the boundary and initial conditions are:

( ) ∞→→ ztzxcp as0,, , (7)

( ) ( )txctxc sp ,,0, = , and (8)

( ) 00,, =zxcp . (9)

The output quantities are the fluxes at x = L:

( )Lx

sss x

cDcubtf

=

∂∂−= ~~2 (10)

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( )Lx

mmm x

cDcubtf

=

∗∗

∂∂−= 2 . (11)

The solution method implemented in COLLAGE II uses a Laplace transform for theequations for solute, mobile and immobile colloids and the rock matrix. Thistransforms the equations into a more manageable form and requires theimplementation of inverse Laplace transform routines to obtain the quantities given inEquations (10) and (11).

The model represented by Equations (1) and (2) is a fairly standard form. However,the kinematic terms which allow for reversible sorption are a notable feature. In theabsence of colloids, Equation (1) reduces to a form which is similar to that used in theSKB far-field model FARF31 (Lindgren and Lindström, 1999) for modellingadvective/dispersive radionuclide transport in a 1-D fracture in the SR97 PA.

2.4 COLLAGE II Parameterisation

Consistent with the aim of determining the conditions under which colloid-facilitatedtransport could lead to potentially significant releases of radionuclides on colloids, thecalculations carried out with COLLAGE II have not sought to calculate absolutevalues of radionuclide flux. Rather, the focus has been on the comparison of therelease flux on colloids to that in solution (both in time and magnitude). Comparisonshave also been made between results from cases with colloid transport, and caseswhere there are no colloids present in the modelled system.

Bentonite is widely considered to be an excellent filter of colloids. Where it is used asa buffer in waste repository designs, it is considered unlikely that near-field generatedcolloids would escape into far-field groundwaters (Kurosawa et al., 1997).Radionuclides diffusing through the bentonite are therefore expected to enter thefracture at x = 0 in solution only.

In modelling the NTS case, the nature of the source term is essentially unknown. Anuclear explosion may embody some of the features of a δ-function input, at least incomparison with the 30 years elapsed since the detonation. The possibility of promptinjection over the 1.3-km transport distance may be discounted, although suchtransport over shorter distances may have occurred (Wickham et al., 2000). Thecolloids found at the NTS comprised a mixture of clays, zeolites, silica and glass(Thompson, 1998). It is possible that colloids were formed as a consequence of theexplosion, and that Pu was released into the local groundwater system on colloids.This possibility may be modelled in COLLAGE II through use of the η parameter.

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The partition parameters used in COLLAGE II are generally not what is reported inthe literature. In practice, the derivation of k1 and k2 in the modelling work reportedhere has assumed that the radionuclide partitioning factor for mobile colloids is

mpKk α=1 [-]. (12)

The factor Kp [m3 kg-1] is the radionuclide-colloid distribution coefficient (analogous

to Kd) and mα [kg m-3] is the suspended load of mobile colloids.

The role of immobile colloids in groundwater systems such as the SR97 fractures ispoorly constrained and it is not clear how immobile colloids could be detected in fieldmeasurements. There are techniques for determining their potential presence inlaboratory rock samples but the implications of the results for colloids in naturalsystems is not clear. For consistency we have adopted the following form fordetermining k2:

fpKk α′=2 [-], (13)

where the population fα [kg m-3] is now the fixed colloid mass per unit volume of

water in the fracture. To allow for the possibility that sorption of solute-phaseradionuclides onto immobile colloids might differ from that onto mobile colloids, weassume that the sorption parameter ( pK ′ [m3 kg-1]) may have a different value to Kp.

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3 Modelling NTS Conditions with COLLAGE II

3.1 Background

At the Nevada Test Site (NTS), colloids bearing plutonium have been found inboreholes. The isotopic composition of the plutonium has been used to identify it asoriginating from the BENHAM nuclear test, 1.3 km away, which took place in the1960s (Kersting et al., 1999). The implication is that plutonium has migrated ingroundwater over a distance of 1.3 km in around 30 years since the test, and thatmigration could have been facilitated by attachment to colloids. The concentration ofcolloids in the groundwater samples is low. Nevertheless, the result indicates thepotential role of colloids in transporting radionuclides rapidly over fairly largedistances. Wickham et al. (2000) provide a more thorough review.

The NTS monitoring data do not include concentrations of Pu on colloids as afunction of time, nor is the nature of the source term definitively established.However, there are sufficient data to allow COLLAGE II to be used in a semi-quantitative assessment of colloid-facilitated transport at the NTS.

First, it is of interest to see if COLLAGE II can produce results consistent with 1.3 kmtransport of colloid-associated Pu in 30 years. Second, it is relevant to ask what theimplications are for the set of model parameters and features, events and processes(FEPs) that allow COLLAGE II to represent the NTS observations.

3.2 Database

In this subsection, we describe the selection of COLLAGE II parameters used tomodel NTS colloid transport.

3.2.1 Fracture and Groundwater

New data on groundwater composition are available from the NTS monitoringprogramme (e.g., Sawyer et al., 1999; Brachmann and Kersting, 2000): the data arerelevant to the BENHAM test and to other locations within the NTS. Monitoring ofgroundwater characteristics and radionuclide migration following the CHESHIRE testwas more detailed than any other test at the NTS. Many of the data from CHESHIREare relevant to the BENHAM case since conditions are locally similar. The YuccaMountain site characterisation programme, geographically adjacent to the NTS, alsoprovides much relevant information (US DOE, 1998).

In using COLLAGE II, the first stage is to assign values to the fracture parameters. Inthis exercise, the length of the fracture was assumed to be 1.3 km and a suitable rangeof groundwater velocities was taken as 1 - 80 m y-1 (Blankennagel and Weir, 1973).From this we take 40 m y-1 as the central value. For dispersion in the groundwater, thevalue quoted by Grindrod et al. (1992) has been used (50 m2 y-1).

10

The host rock surrounding the fracture is porous tuff and therefore the base casemodel simulates diffusion of dissolved Pu tracer into the rock matrix, where it maybecome sorbed. The porosity of the tuff is relatively low - US DOE (1998) quoted atriangular distribution for this type of material. The central value of porosity, φ = 0.02[-], is adopted here. For model testing, the rock diffusivity is assumed to be the sameas that used in the original COLLAGE II test cases - D = 7.9×10-4 m2 y-1. A typicalfracture half-width for the system is 5×10-5 m, which is the central value provided byUS DOE (1998).

We assume that the half-life of the plutonium isotopes is long, compared to the 30-year timescale of the observations, and we therefore set the decay constant to zero.Retardation is set to 106, consistent with the range of Kd values cited for Pu byUSDOE (1998).

The numerical values are summarised in Table 3.1 alongside the data for the colloids.

3.2.2 Colloids

Colloids may move with a velocity that is higher or lower than the mean groundwatervelocity. However, as there are little data with which to assign a priori colloidvelocities, we use the same velocity for colloids as for groundwater (40 m y-1). Inrecent colloid tracer experiments, Wolfsberg and Reimus (2000) successfullyemployed unmodified colloid velocity and dispersion parameters derived from non-sorbing solute tracer experiments to their fitting of colloid breakthrough curves. Wetake as default for the value of colloid dispersion the value quoted by Grindrod et al.(1992), which was used in the COLLAGE II test phase. The value is ∗D = 140 m2 y-1.

The partition coefficient for mobile colloids in COLLAGE II is defined by theradionuclide-colloid sorption coefficient and the suspended colloid load ingroundwater (Equation (12)). The Yucca Mountain TSPA Viability Assessment againprovides a good deal of information in this area (US DOE, 1998). There has beenmuch experimental work in relation to colloids. A range of values is cited for theradionuclide-colloid sorption coefficient (Kp). US DOE (1998) considered 1- 1000 m3

kg-1 to be an appropriate range for plutonium. For the default case we take Kp = 100m3 kg-1, the same as is used in the KBS-3 calculations (Section 4).

Brachmann and Kersting (2000) give details of measurements carried out ongroundwaters abstracted from wells in the NTS as part of the CHESHIRE testmonitoring programme. The data presented are groundwater concentrations ofcolloids together with values for particle size. These data can be used to estimate theparameter, αm [kg m-3], used to derive the partitioning in COLLAGE II.

11

Table 3.1: Reference dataset for the representation of the BENHAM fracture. Thesedata are used as the basis for the set of investigative COLLAGE II runs inSection 3.3. Shaded entries denote FEPs not modelled in this project.

Parameter Value Units Justification

u~ 40 m y-1 The NTS groundwater flow velocity is between 1 and 80 m a-1

(Blankennagel and Weir, 1973) and this represents a central value.

D~ 50 m2 y-1 Taken from Grindrod et al. (1992).

φ 0.02 - Middle value of triangular distributions specified in Table 3-20 ofVolume 3 of the TSPA-VA (US DOE, 1998).

λ 0.0 y-1 In the 30-year time period considered, decay of 242Pu is negligible.

R 106 Suitable value with φ and assuming rock density = 2.65×103 kg m-3

Kd of plutonium in the 5 - 10 m3 kg-1. This value is the same as is

assumed in the KBS-3 modelling in Section 4.

D 7.875×10-4 m2 y-1 Value used in calculations presented in Grindrod et al. (1992).

L 1300 m This is consistent with there being no prompt injection and a directconnection between the explosion site and the measurement location,or prompt injection plus tortuosity of the flow path through aconnected network of fractures.

b 5×10-5 m Geometric mean specified in Table 3-18 of Volume 3 of the TSPA-VA (US DOE, 1998).

n 1 - Downstream boundary at 1,300 m.

∗u 40 m y-1 Colloids may move with a velocity that is higher or lower than themean groundwater velocity. However, as there are little data withwhich to assign a priori colloid velocities, we use the same velocityfor colloids as for groundwater

∗D 140 m2 y-1 Taken from Grindrod et al. (1992).

k1 5.9 - Table 3.3.

k2 0 - Only mobile colloids considered.

1κ 3 y-1 See text.

2κ 0 y-1 Only mobile colloids considered.

β 0 - Only mobile colloids considered.

η 0 - All release assumed on colloids

12

Table 3.2: Colloid load in NTS groundwaters. Colloid density is assumed to be 2650kg m-3. Data from the CHESHIRE test monitoring programme(Brachmann and Kersting, 2000).

wellparticle size

dm [nm]particle density

Nm [particles m-3]colloid loadαm [kg m-3]

ER-20-5 #1 91 3×1016 3.1×10-2

ER-20-5 #3 81 8×1016 5.9×10-2

Table 3.3: Radionuclide partition coefficient, k1, used in modelling the NTS case,based on the colloid load given in Table 3.2. The reference value for k1 inthe NTS modelling is 5.9, and is indicated in bold type.

Colloid sorption coefficient, Kp [m3 kg-1]

1 10 100 1000

3.1×10-2 3.1×10-2 3.1×10-1 3.1 31.0colloid load ingroundwaters

αm [kg m-3] 5.9×10-2 5.9×10-2 5.9×10-1 5.9 59.0

13

The average colloid size is 91 nm (well reference: ER-20-5 #1) and 81 nm (ER-20-5#3). In the two wells, ER-20-5 #1 has an average of 3.0×1010 particles ml-1 (3×1016

particles m-3) and ER-20-5 #1 has 8×1010 particles ml-1 (3×1016 particles m-3). Thesedata are summarised in Table 3.2.

The groundwater-colloid load is therefore given by:

3

6

1mmmmmmm dNvN πρρα == (14)

where the number of mobile colloids is Nm [particles m-3], mρ [kg m-3] is the density

of the free colloidal material, vm [m3] is the volume of each particle, and dm [m] is thediameter of the particles. With these values, a range of k1 values for use in COLLAGEII calculations is shown in Table 3.3.

There are many uncertainties in this database. At this stage it was not felt that the roleof fixed colloids could be reasonably investigated owing to a lack of data. The pres-ence of mobile colloids may be relatively easily determined in groundwater samples.However, by definition these are mobile rather than immobile colloids, which arebound to the rock and are therefore not extracted. The tendency for colloids to attachto fracture walls can be demonstrated in the laboratory but it is another matter to infersuitable values for deep hydrogeochemical conditions. For these reasons we assumeno fixed colloids and set the immobile colloid parameters, k2 and β, to be equal tozero. Similarly we set the sorption/desorption rate onto immobile colloids (κ2) to beequal to zero.

The kinematic aspects of COLLAGE II are an important part of the code. Grindrodand Cooper (1993) tested the model with a range of values. Colloid modelling work inrelation to radioactive waste performance assessments in the past decade has assumedreversible and irreversible sorption (e.g., Allard et al., 1991; Nagra, 1994; JNC,2000). Recent DOE research has provided information on rate constants for the sorp-tion of actinides on colloids. These data can be used to set COLLAGE II rate pa-rameters.

Lu et al. (2000) have recently studied the adsorption of actinides onto colloids. Part ofthe investigation involved measuring both the rate of adsorption and desorption onto avariety of colloidal materials (hæmatite, montmorillonite and silica) in natural andsynthetic groundwaters. The results allow suitable estimates of the COLLAGE II pa-rameter, κ1 [y-1], to be inferred. Values for the radionuclide-colloid sorptioncoefficient are also determined. The plot is reproduced in Figure 3.1.

In the experiments of Lu et al. (2000), the kinetics of adsorption to colloids are com-plex and rates of sorption and desorption are not necessarily of the same form as as-sumed in the COLLAGE II mathematical model. For montmorillonite in naturalgroundwaters, only around 50% of the Pu (V) had been sorbed after 240 hours andthere was an increasing trend which, if extrapolated to 100%, would imply

14

κ1 = 3 y-1. More detailed interaction was observed on timescales of a few tens ofhours (≈ 900 y-1). Sorption onto silica was also observed not to have reached equilib-rium by the end of the experiments at 240 hours, though results for hæmatite indicatedequilibrium at around 100 hours (≈ 90 y-1). Over the timescale of these experiments,the Kp distribution coefficient for Pu was around 100 m3 kg-1 for hæmatite but only5.8 m3 kg-1 for montmorillonite.

Based on the results of Lu et al. (2000), a value of κ1 = 3 y-1 is adopted for plutonium.From these results there is no evidence that the rate would be significantly slower, buta faster rate is possible. The US DOE (1998) values for Kp were considered applicablesince they are derived from similar rock types under comparable conditions to those atthe BENHAM site. For the calculations a value of 100 m3 kg-1 (as in the KBS-3 mod-elling) was used.

The experiments were carried out using colloid concentrations of 200 mg litre-1 (0.2kg m-3). This is higher (by a factor of 3 to 6) than the groundwater colloidconcentrations measured by Brachmann and Kersting (2000). It is not clear if this hasany influence on the Kp value or the kinetics.

Figure 3.1: Kinetics of plutonium - groundwater interactions (from Lu et al., 2000).The percentage of 239Pu adsorbed onto colloids in a variety of natural andsynthetic groundwaters. Montmorillonite in natural groundwater is used asthe basis for the selection of a sorption/desorption rate of 3 y-1.

15

As mentioned above, the exact nature of the source term is not clear. In the referencecases calculated we assume that all radionuclides are input to the fracture already at-tached to colloids, so that η = 0, except in case NTS_ref_NC where it is assumed thatthere is no colloidal material present in the fracture and radionuclides are released andtransported in solution. Other cases in which radionuclides are released in solutiononly are listed in Table 3.5 and for these cases, η = 1. The colloid parameters aresummarised together with the fracture values in Table 3.1.

3.3 Results

The reference data in Table 3.1 allows a number of informative cases to be run. Re-sults are summarised in Figure 3.2. These concentrate on the reference dataset(NTS_ref), for which both the flux on colloids and in solution are plotted, and twovariant cases, summarised in Table 3.4. In the first of these (NTS_ref_NC), it is as-sumed that there is no colloidal material present in the fracture and that radionuclidesare released and transported in solution. There is a strong interaction with the fracturewalls and retardation is effective to the extent that the breakthrough would peak be-yond 1010 years and at low levels.

In the second (NTS_ref_irrev), all radionuclides are assumed to be released on colloi-dal material but there is irreversible sorption so that there is no desorption into solu-tion. All radionuclides are transported on colloids, and there are no radionuclides insolution. Breakthrough is comparatively rapid. Unfortunately, in this case, numericalinstabilities in the COLLAGE II output are apparent. While it is possible to identifythat the colloids contribute to a fairly high flux at times around 30 years, it is notpossible to identify clearly the centroid of the initial peak. The tail of the release issimilarly noisy1.

With the large difference in behaviour between the two extremes, it is clear that therole of the sorption/desorption rate (κ1) is of interest. Another feature of the modellingis that it is assumed that the release is on colloids. There remains the alternative pos-sibility that the Pu has entered the system in solution and has subsequently becomeattached to colloids.

Two series of additional results have been calculated (summarised in Table 3.5)which explore the role of the rate constant κ1 and the release form - radionuclides oncolloids or in solution. A range of sorption rates has been studied with 10-3 ≤ κ1 ≤ 103

y-1. To contrast with the reference case assumption, the second set of runs assumesthat all radionuclides are input in solution, with transfer to colloids by sorp-tion/desorption.

The total flux released is shown in Figure 3.3 (release on colloids) and Figure 3.4(release in solution).

1 The peak can be smoothed but only if the colloid dispersion coefficient D* ≥ 1000 m2 y-1. Using thisvalue of D* resolves the peak but it has not been included because the value is unrealistically high.

16

Table 3.4: Variations on the NTS reference case dataset considered in theinvestigation of the properties of the COLLAGE II representation of theNTS system.

Case characteristics/comments

NTS_ref The reference case as defined in Table 3.1.

NTS_ref_NC Data as in Table 3.1, no colloids (k1 = κ1 = 0.0), Release in solution (η = 1.0).

NTS_ref_irrev Reference case data set (Table 3.1) with irreversible sorption (κ1 = 0.0), allrelease on colloids ⇒ no release in solution.

��

1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x10 8 1x10 9 1x10 10 1x10 11 1x10 12

tim e [a ]

1x10 -12

1x10 -11

1x10 -10

1x10 -9

1x10 -8

1x10 -7

1x10 -6

1x10 -5

1x10 -4

1x10 -3

1x10 -2

1x10 -1

1x10 0

rele

ase

flux

[m

ol m

-2 a

-1]

n o co llo id s - N T S _ re f_ n c

so lu te f lu x - N T S _ re f

co llo id f lu x - N T S _ re f

co llo id f lu x - N T S _ re f_ irrev

Figure 3.2: Plutonium transport in the NTS reference fracture for a variety ofconditions. With no colloids present in the system, releases would occurfar into the future as a consequence of the high retardation assumed for Puin solution on fracture surfaces. The shaded region indicates times greaterthan one million into the future and demonstrates that releases with nocolloids have little significance in terms of performance assessment.

17

Table 3.5: Summary of NTS simulation test cases investigating the role ofsorption/desorption kinetics and the form of the release to the fracture.Modifications with respect to the reference case in Table 3.1 are noted.

case characteristics

NTS_k1_1e-3 κ1 = 10-3 y-1, η = 0.0

NTS_k1_1e-2 κ1 = 10-2 y-1, η = 0.0

NTS_k1_1e-1 κ1 = 10-1 y-1, η = 0.0

NTS_k1_1 κ1 = 1 y-1, η = 0.0

NTS_k1_10 κ1 = 10 y-1, η = 0.0

NTS_k1_100 κ1 = 100 y-1, η = 0.0

rele

ase

on c

ollo

ids

NTS_k1_1e2 κ1 = 103 y-1, η = 0.0

NTS_k1_rs_1e-3 κ1 = 10-3 y-1, η = 1.0

NTS_k1_rs_1e-2 κ1 = 10-2 y-1, η = 1.0

NTS_k1_rs_1e-1 κ1 = 10-1 y-1, η = 1.0

NTS_k1_rs_1 κ1 = 1 y-1, η = 1.0

NTS_k1_rs_10 κ1 = 10 y-1, η = 1.0

NTS_k1_rs_100 κ1 = 100 y-1, η = 1.0

rele

ase

in s

olu

tion

NTS_k1_rs_1e2 κ1 = 103 y-1, η = 1.0

18

3.4 Discussion

Figure 3.2 shows that the reference case (open circles) cannot reproduce the NTS ob-servations. After 30 years, the colloid concentration is vanishingly small, much lowerthan the concentrations of Pu on colloids reported by Kersting et al. (1999). The ref-erence case data set does indicate that colloid-facilitated transport could have an effecton both the colloid-borne and solute fluxes of Pu at the end of the fracture but only attimes very far into the future (> 500 million years). There is a two order of magnitudeincrease in the peak release compared to the case with no colloids but the result is stillat a very low level. Given that plutonium-bearing colloids have apparently travelled1.3 km in 30 years at the NTS, and are present in detectable quantities, it is clear thatthe reference dataset does not represent the observations satisfactorily.

The fourth curve in Figure 3.2 (diamonds) illustrates an alternative model calculationin which colloids do transport radionuclides over the 1.3 km distance from theBENHAM test to the sampling point. In this example, radionuclides must enter thefracture in colloidal form and the kinetics of desorption must proceed at very lowrates compared to those inferred from the work of Lu et al. (2000).

In Figure 3.3, a range of curves for various values of κ1 is shown, with radionucliderelease exclusively on colloids. These suggest that for κ1 in the range 10-3 to a fewtimes 10-2 y-1, an early peak in the release flux may be anticipated. If κ1 is 0.1, theinitial peak is no longer seen and above around κ1 = 1.0 y-1 there is no earlybreakthrough at all.

The results plotted in Figure 3.4 are for the case in which all radionuclides are re-leased in solution. In model runs where the release is in solution, it is generally notpossible to obtain an early peak. Nevertheless, some breakthrough of radionuclides atearly times is still observed, for κ1 in the range 10-3 to 10-1. It is therefore possible thatthe NTS inferences of rapid Pu transport could also be associated with release in so-lution, and sorption/desorption at a rate of around 10-2 y-1.

Note that if the release of Pu were in solution and the sorption irreversible (κ1 = 0.0),there would then be no release on colloids and no colloid-born plutonium would havebeen detected. For release in solution, the only results predicting rapid transport of Puare for the limited range of κ1 specified above. These results suggest that theBENHAM test probably introduced radionuclides into the fracture that were alreadyassociated with colloids.

No breakthrough curve has been measured at the BENHAM observation wells to datebut, were it possible to measure it in future, the rate of change of plutonium concen-tration could be used to better constrain the source term. If the fall-off were rapid, itwould correspond to the situation in Figure 3.3 and might add additional support forthe suggestion that the release was probably on colloids. If the fall-off was slower, therepresentation in Figure 3.4 could be more appropriate, and this might add support forthe input of plutonium being in solution.

19

��

��

1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x10 8 1x10 9 1x10 10 1x10 11 1x10 12

tim e [a ]

1x10 -18

1x10 -17

1x10 -16

1x10 -15

1x10 -14

1x10 -13

1x10 -12

1x10 -11

1x10 -10

1x10 -9

1x10 -8

1x10 -7

1x10 -6

1x10 -5

1x10 -4

1x10 -3

1x10 -2

1x10 -1

1x10 0

rele

ase

flux

[m

ol m

-2 a

-1]

so rp tio n /d e so rp tio n ra teκ1 = 1 0 -3 y -1

κ1 = 1 0 -2 y -1

κ1 = 1 0 -1 y -1

κ1 = 1 y -1

κ1 = 1 0 y -1

κ1 = 1 0 2 y -1

κ1 = 1 0 3 y -1

Figure 3.3: Influence of radionuclide-colloid sorption/desorption rate on radionucliderelease flux (solute + colloid) at the NTS. Case of all radionuclide releaseon colloids.

��

��

1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x10 8 1x10 9 1x10 10 1x10 11 1x10 12

tim e [a ]

1x10 -18

1x10 -17

1x10 -16

1x10 -15

1x10 -14

1x10 -13

1x10 -12

1x10 -11

1x10 -10

1x10 -9

1x10 -8

1x10 -7

1x10 -6

1x10 -5

1x10 -4

1x10 -3

1x10 -2

1x10 -1

1x10 0

rele

ase

flux

[m

ol m

-2 a

-1]

so rp tio n /d e so rp tio n ra teκ1 = 1 0 -3 y -1

κ1 = 1 0 -2 y -1

κ1 = 1 0 -1 y -1

κ1 = 1 y -1

κ1 = 1 0 y -1

κ1 = 1 0 2 y -1

κ1 = 1 0 3 y -1

Figure 3.4: Influence of radionuclide-colloid sorption/desorption rate on radionucliderelease flux (solute + colloid) at the NTS. Case of all radionuclide releasein solution.

20

It is possible that the underground nuclear explosion gave rise to abundant colloid-sized particles, effectively instantaneously. Such a theory is supported by therelatively high colloid concentrations observed at the NTS by Brachmann andKersting (2000), which are in excess of the theoretical limit of 0.01 kg m-3 suggestedby Degueldre (1994) on the basis of groundwater hydrogeochemistry. This could berepresented in COLLAGE II by increasing the partitioning parameter k1. The highvalues at the NTS may represent a groundwater system perturbed from its naturalstate by the nuclear detonations and it may be the case that the groundwater colloidloads will return to a lower level with time.

Two alternatives are considered in Figure 3.5: k1 = 103 and k1 = 106. Both cases areplotted for the reference sorption/desorption rate: κ1 = 3 y-1 and for κ1 = 10-2. In thecase of very high k1 (106), an early pulse occurs with either value of thesorption/desorption parameter. With k1 = 1000, an early peak only occurs with the lowvalue of κ1.

The likelihood of such high values of the partitioning coefficient is open to question.Degueldre’s (1994) work implies k1 ≈ 1 is an upper limit. The high values of k1 inFigure 3.5, although possibly representative of conditions subsequent to anunderground nuclear test, cannot meaningfully be applied to conditions in anundisturbed geosphere.

��

1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x10 8 1x10 9 1x10 10 1x10 11 1x10 12

tim e [a ]

1x10 -12

1x10 -11

1x10 -10

1x10 -9

1x10 -8

1x10 -7

1x10 -6

1x10 -5

1x10 -4

1x10 -3

1x10 -2

1x10 -1

1x10 0

rele

ase

flux

[m

ol m

-2 a

-1]

n o co llo id s

κ1 = 3 y -1, k 1 = 1 0 3

κ1 = 1 0 -2 y -1, k 1 = 1 0 3

κ1 = 3 y -1, k 1 = 1 0 6

κ1 = 1 0 -2 y -1, k 1 = 1 0 6

Figure 3.5: COLLAGE II output for artificially increased values of the partitioningcoefficient k1. In these examples the value of k1 is at a level not supportedby observed data for undisturbed geospheres (see text). Release fluxshown is solute + colloid.

21

If the BENHAM test generated large amounts of colloids, under such circumstances itmight be imagined that colloids would become rapidly attached to the fracture wallsand that the colloid load would change with time. However, this process is notcurrently represented in COLLAGE II and the scenario cannot be exploredquantitatively.

A scenario in which radionuclides are introduced into the fracture only on colloids isthe favoured modelling option for explaining the NTS interpretation of km-scale Pu-colloid transport in 30 years. This, combined with a low sorption/desorption rate, isthe most likely explanation of the BENHAM observations. Without access to areasonable breakthrough curve for plutonium on colloids in the NTS wells, this is asfar as the current analysis can go. The implications of this analysis for Swedish wastedisposal assessments are considered in the following section.

22

4 The Potential Influence of Colloids in Swedish PAs

4.1 Background

Svensk Kärnbränslehantering AB (SKB) has responsibility for disposal of Sweden’sradioactive waste. For the disposal of spent nuclear fuel, SKB has developed theKBS-3 concept. In the KBS-3 concept, SKB plans that after 30 to 40 years of interimstorage, spent fuel will be placed in copper canisters, surrounded by a bentonitebuffer, and disposed at a depth of about 500 m in crystalline bedrock.

The KBS-3 repository for spent nuclear fuel is composed of a system of barriers. Thefuel is placed in copper canisters, surrounded by a layer of bentonite clay. The clayprovides mechanical protection, and limits access of groundwater and corrosivesubstances to the canisters. The bentonite also adsorbs radionuclides that may bereleased from the canisters, and filters colloids that may form within the repository.

Kurosawa et al. (1997) indicate that any colloidal material generated in the near-fieldwill be effectively filtered by the bentonite layer. Any radionuclides migratingthrough the bentonite will therefore probably enter groundwater flow systems insolution rather than already attached to colloids. This provides a contrast with ourconsideration of the NTS system, in which we suggest that the radionuclides wereprobably released in colloidal form. COLLAGE II can represent cases in which theradionuclides are initially dissolved, or are initially colloidal, using the parameter η,the fraction of the radionuclide release in solution.

The repository host rock in Sweden is granite whereas at the NTS it is volcanic tuff.Nevertheless, Wickham et al. (2000) compared the mineralogy of the two sites andfound that they are similar, though texturally contrasting. Radionuclide transportproperties may also be similar in the two systems. Retardation will be higher in theKBS-3 granite because the matrix porosity is lower than the NTS tuff (10-5 comparedwith 0.02), although retardation is already high in the NTS dataset.

The aim of the analysis presented in this section is to discover regions of parameterspace where colloids might play a role. In order to achieve this objective, bothdeterministic and probabilistic sensitivity analyses have been carried out. Attentionagain focuses on plutonium which, as an actinide, is expected to sorb strongly tocolloids (Degueldre, 1994). Other actinides tend to have similar properties, and arediscussed in Section 4.4.

4.2 Colloid Transport in the KBS-3 Concept

4.2.1 Model Parameterisation

In this section we describe how we have parameterised the COLLAGE II model sothat it can be used to represent the transport of plutonium through the fracturedgeosphere present in the KBS-3 disposal concept. The basis for our parameterisation

23

is derived from the geosphere modelling carried out by Lindgren and Lindström(1999) in the SR97 assessment using the geosphere code FARF31, which considers aone-dimensional representation of a planar fracture.

The SR97 assessment considers three hypothetical sites. The geosphere transportproperties of these sites differ principally in terms of the fracture flow path lengthconsidered in the assessment. For this analysis we choose the shortest of these - theAberg site - as the basis for the representation of the fracture.

One way in which the FARF31 and COLLAGE II mathematical models differ is inthe way in which the total flow in the fracture is represented. In SR97 the F-ratio isused, which is the product of the groundwater travel time and the flow-wetted surfacearea per unit volume of water. The F-ratio is related to the fracture aperture half-width (b [m]) used by COLLAGE II and may be used to account for transport inmultiple fractures. As COLLAGE II considers only a single fracture, we use the datain Table 3-14 of Lindgren and Lindström (1999) in which two fractures are defined,one with width 10-4 m, and the other with width 5×10-4 m. For COLLAGE II we use2b = 2×10-4 m on this basis.

In the KBS-3 concept, the repository is at a depth of 500 m and the simplestassumption is for a fracture of this length reaching down to the excavation disturbedzone (EDZ) and through which water can flow. There is no discussion of the relevantflow path length in Lindgren and Lindström (1999), and we therefore take a pathlength L = 500 m.

The groundwater travel time corresponds to 500 m in ten years, according to Lindgrenand Lindström (1999). However, Appendix 1 of Skagius et al. (1999) quotes aporewater velocity of up = 30 m y-1 and this has been adopted as the base case value.There is scope for alternative values but the implications for solute transport are notparticularly important (see Section 4.3).

Lindgren and Lindström (1999) quoted a Peclet number of 10 and this is similar toassessments elsewhere. Nagra (1994) used this value to define dispersion despite themisgivings about the low value (cf. de Marsily, 1986). The relationship:

Le a

LP = [-], (15)

is used, where the dispersivity is aL (longitudinal dispersivity). L is the flow pathlength, as above. With this relationship, the dispersivity for COLLAGE II is L/Pe =500/10 = 50. Hence, the dispersion coefficient is given by

1-23

y m 695.110

5003010131~ =×××⋅====−

epflowpflowD P

LuudduD εε , (16)

where the flow porosity εflow [-] is 1.13×10-3 (Lindgren and Lindström, 1999).

24

Kd values for plutonium are taken from Lindgren and Lindström (1999). For Pu, therock diffusivity is quoted as 4×10-14 m2 s-1. The rock Kd of Pu is 5 m3 kg-1. Togetherwith the rock matrix porosity of 5×10-3, this gives a retardation factor of 2.69×106.The rock density quoted is 2.7×103 kg m-3.

The parameter values used in the COLLAGE II modelling are summarised in Table4.1.

It is assumed here that there are no immobile colloids. This simplifies the task of dataselection because the colloid component of the model is based on the release form, thevelocity and dispersion parameters for the colloidal particles, the partitioning ofradionuclides in solution, and the sorption/desorption rate.

Following the analysis given by Grindrod (1989), it is assumed here that colloidsmove in the centre of the flow channel and so the mean velocity is higher than for thewater flow averaged across the aperture. The ratio of colloid velocity to water velocityhas been set at 1.3:1. The alternative use of ∗= uu~ was employed in the NTScalculations, corresponding to the assumption of Wolfsberg and Reimus (2000). Herewe took the higher value from Grindrod (1989) so as to be able to exercise anadditional feature of the conceptual model. However, in the probabilistic sensitivityanalysis (Section 4.3) the use of the factor of 1.3 instead of 1.0 is shown to berelatively unimportant.

Values for the dispersion coefficient are taken from Grindrod and Cooper (1993).Values for the kinetics of sorption/desorption are based on the review of Lu et al.(1999) as discussed in Section 3.2.2; the rate assumed is κ1 = 3 y-1.

Given the nature of the release from the bentonite buffer in the KBS-3 concept, it isassumed that all radionuclides enter the fracture already in solution so that (in contrastto some of the NTS calculation cases) η = 1.0.

As there are no immobile colloids, all parameters relating to them are set to zero.

Radionuclides are assumed to enter the fracture in solution and it may therefore beassumed that the colloidal content of the fracture groundwater is unperturbed from itsnatural state. Laaksoharju et al. (1995) have noted that the concentrations in typicalSwedish groundwaters are very low. Colloid concentration may be estimated based onlocal hydrogeochemical conditions (Degueldre et al., 2000). Currently the conditionsare somewhat saline. The possibility of increased colloid loads may be associatedwith an influx of non-saline waters under a future glacial melting scenario. However,the impact is not expected to be large.

25

Table 4.1: Reference dataset for the representation of an Aberg fracture inCOLLAGE II. Shaded entries denote FEPs not modelled in the project.

Parameter Value Units Justification

u~ 30.0 m y-1 Skagius et al. (1999)

D~ 1.695 m2 y-1 Lindgren and Lindström (1999), based on a Peclet number of 10.

φ 5×10-5 - Lindgren and Lindström (1999).

λ 1.86×10-6 y-1 Value for 242Pu (Lindgren and Lindström, 1999).

R 2.69×106 - Derived from other properties. Matrix kd and rock density fromLindgren and Lindström (1999).

D 1.262×10-6 m2 y-1 Lindgren and Lindström (1999).

L 500 m Lindgren and Lindström (1999).

b 10-4 m Single fracture interpreted from Lindgren and Lindström (1999),Table 3-14.

n 1 - Downstream boundary at end of fracture, see Section 3.2.1.

∗u 39.6 m y-1 Assumes that colloids move in centre of the aperture

∗D 4.746 m2 y-1Using ratio of 140/50 relative to D

~ , cf. Grindrod & Cooper, (1993)

k1 2.0×10-3 - See text for details.

k2 0 - Only mobile colloids considered.

1κ 3.0 y-1 Default value from the Yucca Mountain analysis (see Section 3.2.2)

2κ 0 y-1 Only mobile colloids considered.

β 0 - Only mobile colloids considered.

η 1.0 - All release assumed in solution - see text.

26

Table 4.2: Values for colloid load (αm) in a variety of fractured granites. Thereference case is denoted by the bold type.

source µg ml-1 kg m-3 comments

0.002 2.0×10-6 extreme low range - factor of 10 lower thansaline case

Assumed for sensitivityanalysis

0.0045 4.5×10-6 factor of 10 lower than non-saline case

Laaksoharju et al. (1995) 0.02 2.0×10-5 50 - 500 nm, saline groundwaters (present day)

0.045 4.5×10-5 non-saline groundwaters - glacial meltwaterdilution

0.2 2.0×10-4 high range for Swedish conditions - factor of 10higher than saline case

Assumed for sensitivityanalysis purposes

0.45 4.5×10-4 high range for Swedish conditions - factor of 10higher than non-saline case

0.1 1.0×10-4 lower detection limits for Swiss granites

0.4 4.0×10-4 lower detection limits for Swiss granitesCanadian, French and Spanish

Degueldre (1994)

10 1.0×10-2 value quoted for special circumstances of verylow Na and Ca content in groundwaters

Table 4.3: Values of the radionuclide - colloid partition coefficient (k1) for a range ofradionuclide - colloid sorption coefficients (Kp) and colloid loads (αm).The reference case value for saline conditions is indicated in bold type.

αm [kg m-3]

Kp [m3 kg-1] 2.00×10-6 4.50×10-6 2.00×10-5 4.50×10-5 2.00×10-4 4.50×10-4

0.1 2.0×10-7 4.5×10-7 2.0×10-6 4.5×10-6 2.0×10-5 4.5×10-5

1 2.0×10-6 4.5×10-6 2.0×10-5 4.5×10-5 2.0×10-4 4.5×10-4

10 2.0×10-5 4.5×10-5 2.0×10-4 4.5×10-4 2.0×10-3 4.5×10-3

100 2.0×10-4 4.5×10-4 2.0×10-3 4.5×10-3 2.0×10-2 4.5×10-2

103 2.0×10-3 4.5×10-3 2.0×10-2 4.5×10-2 2.0×10-1 4.5×10-1

104 2.0×10-2 4.5×10-2 2.0×10-1 4.5×10-1 2.0 4.5

105 2.0×10-1 4.5×10-1 2.0×100 4.5×100 20.0 45.0

27

Table 4.2 summarises the information concerning colloid load in fractured granites.Specifically for Swedish fractures, Laaksoharju et al. (1995), citing Allard et al.(1991), assumed 0.02 µg ml-1 for colloidal particles under present-day salineconditions and 0.045 µg ml-1 for less saline conditions. The difference in the twocolloidal concentrations is small. Table 4.2 also adds some higher and lower valuessuitable for consideration in sensitivity analyses.

As discussed above, Kp values for plutonium are taken from Lindgren and Lindström(1999), and this together with the colloid concentration, determine the partitioncoefficient, k1. Table 4.3 illustrates the choice of a suitable value for k1. As notedabove, the reference case is defined by Table 4.1. Alternative parameter values foradditional cases studied are summarised in Table 4.4.

4.2.2 Model Results and Discussion

Figure 4.1 shows breakthrough curves for the no-colloid case and saline and non-saline groundwaters. These results indicate that the no-colloid case has a long delaybefore radionuclides arrive at the end of the fracture. This is a consequence of highretardation. Based on similar results, Laaksoharju et al. (1995) concluded that colloidswould be unlikely to play a major role in the transport of radionuclides throughfractures. The reference case results for saline groundwaters show that the flux ispredominantly in solution with only a small contribution on colloids. Even in the caseof non-saline groundwaters, the picture is virtually unchanged, and it is difficult todistinguish the three solute fluxes, which give almost identical results.

However, experience in the modelling of the NTS system implies that kinetic effectsmight potentially influence the nature of the breakthrough curve. A sequence of casesfor different low values of κ1 were run, as summarised in Table 4.4. All cases wererun for the release of radionuclides in solution. The resulting breakthrough curves areshown in Figure 4.2.

With slow kinetics of sorption/desorption, it is possible to obtain peaks at early timesthat are comparable in magnitude to the peak at later times. This is illustrated inFigure 4.3. Early releases occur over a relatively restricted range of low values of κ1.At these low rates, even if all plutonium is initially released in solution, a smallamount is able to associate with colloids. Because of the slow rate of disassociation,this plutonium is then able to be carried significant distances along the fracture beforebeing released into solution, where it is rapidly sorbed onto mineral surfaces.

If sorption kinetics are consistent with κ1 being in the range 10-3 to 10-1 yr-1, thenearly releases may be seen, although the actual rate values quoted here are specific tothe particular length- and time-scales analysed.

28

Table 4.4: Variations on the KBS-3 reference case. All release in solution.Parameters modified with respect to the reference case (Table 4.1) areindicated.

case Characteristics

KBS3_ref_nc κ1 = 0.0 y-1, k1 = 0.0, no colloids

KBS3_ref_s κ1 = 3.0 y-1, k1 = 2.0×10-3, saline conditions

fast

sor

ptio

n /

deso

rpti

onra

te

KBS3_ref_ns κ1 = 3.0 y-1, k1 = 4.5×10-3 , non-saline conditions

kap_a κ1 = 10-3 y-1, k1 = 2.0×10-3

kap_f κ1 = 10-2 y-1, k1 = 2.0×10-3

kap_k κ1 = 10-1 y-1, k1 = 2.0×10-3

kap_p κ1 = 1.0 y-1, k1 = 2.0×10-3

vari

able

sor

ptio

n* /

deso

rpti

on r

ate

kap_u κ1 = 10 y-1, k1 = 2.0×10-3

Note:

* Twenty-seven test cases were run kap_a - kap_z plus kap_peak. The dataset was that given in Table4.1 with κ1 logarithmically distributed 5 per decade over the range 10-3 ≤ κ1 ≤ 10 y-1, with kap_peakhaving κ1 = 8×10-2.

29

1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7

tim e [a ]

1x10 -12

1x10 -11

1x10 -10

1x10 -9

1x10 -8

1x10 -7

1x10 -6

rele

ase

flux

[m

ol m

-2 a

-1]

K B S -3 R eferen ce C as eso lu te flu x - n o co llo id s (K B S 3 _ re f_ n c )

so lu te flu x - sa lin e (K B S 3 _ re f_ sa lin e )

co llo id f lu x - sa lin e (K B S 3 _ re f_ sa lin e )

so lu te flu x - n o n -sa lin e (K B S 3 _ re f_ n o n -sa lin e )

co llo id f lu x - n o n -sa lin e (K B S 3 _ re f_ n o n -sa lin e )

Figure 4.1: Results for the KBS-3 reference case. Fast sorption/desorption kinetics (κ1

= 3 y-1), radionuclide release in solution.

1 x10 1 1 x10 2 1 x10 3 1 x10 4 1 x10 5 1 x10 6 1 x10 7

tim e [a ]

1 x10 -12

1 x10 -11

1 x10 -10

1 x10 -9

1 x10 -8

1 x10 -7

1 x10 -6

1 x10 -5

1 x10 -4

1 x10 -3

rele

ase

flux

[m

ol m

-2 a

-1]

r a d io n u c lid e -co llo idso rp tio n /d e so rp tio n ra te

κ1 = 1 0 -3 y -1

κ1 = 1 0 -2 y -1

κ1 = 1 0 -1 y -1

κ1 = 1 .0 y -1

κ1 = 1 0 .0 y -1

Figure 4.2: Effect of low values of the sorption/desorption rate, κ1, on plutoniumbreakthrough curve. Release in solution with all other parameters atreference values (cf. Figure 4.1).

30

1 x10 -4 1 x10 -3 1 x10 -2 1 x10 -1 1 x10 0 1 x10 1

rad io n u c lid e -co llo id so rp tio n -d e so rp tio n ra te , κ1 [y -1 ]

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

peak

col

loid

flu

x / p

eak

flux

(no

col

loid

s)

Figure 4.3: Effect of sorption - desorption rate (• 1) on the colloid-born release at 12.6years for the KBS-3 dataset. Flux on colloids at 12.6 years is normalisedto the peak solute flux seen in the no-solute case (KBS3_ref_nc). Themaximum early release peak is for κ1 = 0.08 y-1.

Figure 4.3 illustrates that there are two regions, one each side of the peak, where κ1

has values implying that there would be no significant radionuclide transport bycolloids:

1) If radionuclides are initially in solution and sorption was very slow or irreversible(κ1 ~ 0.0), as represented by the extreme left of Figure 4.3, then radionuclideswould be virtually unable to sorb to colloids. Colloids would therefore play norole in radionuclide transport.

2) If sorption/desorption was rapid (κ1 > 1), as represented by the right of Figure 4.3,colloids would be sorbed and desorbed from colloids rapidly enough for sorptionon the fracture walls to effectively retard radionuclide transport.

Between these regions is a critical range of values of κ1 for which colloids are able tocarry plutonium a significant distance along the fracture.

If ( ) ( )desorptionsorption11 κκ ≠ more complex effects might be anticipated. However, the

mathematical model in COLLAGE II does not allow this to be modelled.Modifications to COLLAGE II would be needed to evaluate the effects of differentialsorption rates.

31

4.3 Probabilistic Sensitivity Analysis

The key parameters in the COLLAGE II model may all exhibit considerable variation.A probabilistic sensitivity analysis has been conducted to identify those combinationsthat give rise to more significant colloid-facilitated radionuclide transport.

4.3.1 Model Parameterisation

The Sandia Latin-Hypercube Sampling code (LHS) of Iman and Shortencarrier (1984)was used to generate 1000 LHS samples based on variations of the parameters, asdiscussed below. Simple ranges were used in all cases and loguniform distributionsemployed.

Seven parameters were varied; the justification of the values selected is given in Table4.5. Those parameters relating to the fracture itself were not varied. These include theflow velocity and dispersion coefficient of the solute. The fracture half-width was alsokept constant as were the rock matrix porosity and path length. Matrix porosityinfluences the retardation of radionuclides in solution. However, as this is alsodetermined by radionuclide rock Kd, it was the Kd that was varied in order to varyretardation.

4.3.2 Model Results and Discussion

The Kolmogorov-Smirnov test has been used to determine the sensitivity of the modelto the values of the parameters considered. In this test, the output distribution is splitat the median of the input parameter to be tested, and the cumulative distributionfunction (cdf) of the two parts of the output are calculated. Two parameters arecalculated, the absolute difference of the cdfs for the upper and lower parts of theinput distribution, and the probability that the two cdfs are the same.

The results (Table 4.6) show that the key model input determining the impact of thesystem is the partition parameter k1. This parameter was not sampled directly, but isitself dependent on two sampled parameters, the radionuclide - colloid sorptioncoefficient (Kp) and the mobile colloid concentration (αm) in the water in the fracture.The importance of k1 comes as no surprise - the more colloids there are and the morestrongly radionuclides bind to them, the more the peak total flux increases.

To illustrate the influence of Kp and αm further, scatter plots of peak total flux in theno-colloid case vs. sorption coefficient and colloid load are shown in Figure 4.4. Thetime of peak is plotted against Kp in Figure 4.5. Figure 4.6 illustrates the influence ofκ1 on the time of peak flux.

32

Table 4.5: List and justification of parameters sampled in the probabilistic sensitivityanalysis.

Modelparameter Comments and justification

Sampled pdfs andranges

∗u [m y-1] Colloid transport velocity. Grindrod (1989) noted that theratio of mean colloid to mean water velocities is 1.32.This is used as a central figure and one order of magnitudeon either side is allowed for a scaling factor.

scaling factor -loguniform: 0.132 -

13.2

∗D [m2 y-1] Mobile colloid dispersion coefficient. Grindrod et al.(1993) suggested that the ratio is ∗DD

~ = 140/50. This is

used to define ∗D in the reference case. In thesecalculations a scaling factor is used with one order ofmagnitude on either side of the value of the solutedispersion coefficient.

scaling factor -loguniform: 14/50 -

140/5 m2 y-1

R [-] Rock matrix retardation coefficient. Well defined in terms

of the rock matrix Kd: dKR ρ

φφ−+= 1

1 .

rock Kd - loguniform:4.5 - 5.5.

k1, k2 [-] Partition parameters. These COLLAGE II parameters arecombinations of sorption coefficients and the colloid loadin the groundwater (Section 2.4):

pmKk α=1and

bf Kk ′= α2 .

The range for Kp is consistent with the data observed byLu et al. (2000) and takes into account the data set out byDegueldre (1994), but extends the range by an order ofmagnitude on either side. The range of groundwatercolloid concentrations is determined by the rangeidentified in Table 4.2.

Kp - loguniform: 0.1 ≤Kp ≤ 105 m3 kg-1

αm - loguniform: 0.002≤ αm ≤ 0.45 kg m-3

bK ′ = Kp - perfect

correlation

αf - defined byparameter β: αf = βαm.

β [-] Ratio of mobile to immobile colloids. The number ofimmobile colloids is very uncertain. It is not clear howtheir numbers may be estimated from groundwateranalyses carried out by Laaksoharju et al. (1995) orBrachmann and Kersting (2000). Degueldre et al. (2000)do not address immobile colloids in their review ofgroundwater and colloids. A broad range is thereforeassumed corresponding to situations where there are fewermobile colloids to situations where there are moreimmobile than mobile colloids.

loguniform: 10-6 ≤ β ≤103

κ1, κ2 [y-1] Sorption/desorption rate coefficients for mobile andimmobile colloids. From the deterministic sensitivityanalysis carried out above, the sorption/desorption rate formobile colloids was assigned a range 10-3 - 103 per year.Given the uncertainties in the treatment of immobilecolloids, the same range is set and a perfect correlation isassumed.

κ1 - loguniform 10-3 ≤κ1 ≤ 103 y-1,

κ2 = κ1.

33

Table 4.6: Analysis of the probabilistic sensitivity analysis of plutonium transport ina KBS-3 fracture. Kolmogorov-Smirnov test with the input distributionsplit at the median of the output quantity. Absolute difference in cdf andthe probability of the two distributions being the same are shown. Largenegative probability of difference (high negative number) and largedifference indicate sensitivity. Key values are shown in bold type and areshaded. Results for 1000 LHS samples.

KS-difference log10 (KS-probability)

Peak total fluxTime of peak

total flux

Colloid flux tototal flux ratioat time of peak Peak total flux

Time of peaktotal flux

Colloid flux tototal flux ratioat time of peak

Scaling factor forcolloid velocity (u*)

0.2 0.2 0.2 -7 -7 -5

Scaling factor forcolloid dispersion

(D*)0.0 0.0 0.1 0 0 -1

Radionuclide - colloidsorption Kp (mobile &

immobile colloids)0.6 0.6 0.7 -85 -81 -95

Mobile colloid load ingroundwater, αm

0.3 0.3 0.3 -23 -21 -25

Radionuclide - mobilecolloid partitioning

factor, k1

0.8 0.7 0.9 -139 -111 -160

Colloid immobile tomobile population, β 0.0 0.1 0.1 0 -2 -1

Radionuclide -immobile colloid

partitioning factor, k2

0.4 0.3 0.4 -35 -26 -38

Sorption/desorptionrate for mobile and

immobile colloids, κ1

0.1 0.3 0.2 -3 -15 -13

Radionuclide - rockmatrix sorptioncoefficient, Kd

0.5 0.4 0.1 -62 -44 -1

Rock matrixretardation factor, R 0.5 0.4 0.1 -61 -43 -1

34

(a) radionuclide - colloid sorption coefficient, Kp. Extreme ranges of Kp areindicated by shading.

��

��

1x10 -1 1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x105

c o llo id so rp tio n c o effic ie n t K p [m 3 k g -1]

1x10 -1

1x10 0

1x10 1

1x10 2

1x10 3

1x10 4

1x10 5pe

ak f

lux

norm

alis

ed to

no

collo

id p

eak

1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x108co llo id so rp tion co effic ien t K p [m l g -1 ]

R e fere n c eC a se

(b) mobile colloid load in fracture groundwater, αm.

1x10 -6 1x10 -5 1x10 -4 1x10 -3 1x10 -2

c o llo id p o pu la tio n αm [k g m -3]

1x10 -1

1x10 0

1x10 1

1x10 2

1x10 3

1x10 4

1x10 5

peak

flu

x no

rmal

ised

to n

o co

lloid

pea

k

1x10 -1 1x10 0 1x10 1 1x10 2 1x10 3co llo id p o p u la tio n αm [g m l-1]

re fe re nc e sa lineg ro u n d w a ter co n d itio n s

re fere n c e n o n -sa lin eg ro u n d w a ter c o n d itio n s

Figure 4.4: Scatter plots of key parameters showing their influence on peak totalrelease flux. Significance of green diamonds is discussed in the text.

35

��

��

��

1x10 -1 1x10 0 1x10 1 1x10 2 1x10 3 1x10 4 1x10 5

co llo id so rp tio n co e ffic ie n t K p [m 3 k g -1]

1x10 1

1x10 2

1x10 3

1x10 4

1x10 5

1x10 6

time

of p

eak

flux

[y]

1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7 1x10 8co llo id so rp tio n co effic ien t K p [m l g -1 ]

R e fe re n c eC a se

Figure 4.5: Scatter plots of time of peak release vs. radionuclide - colloid sorptioncoefficient, Kp. Extreme ranges of Kp are indicated by shading as is theregion for t < 100 years.

��

1x10 -3 1x10 -2 1x10 -1 1x10 0 1x10 1 1x10 2 1x10 3

so rp tio n /d e so rp tio n ra te κ1 [y -1]

1x10 1

1x10 2

1x10 3

1x10 4

1x10 5

1x10 6

time

of p

eak

flux

[y]

Figure 4.6: Scatter plots of time of peak release vs. sorption/desorption rate, κ1. Theregion for time < 100 years is shaded.

36

Figure 4.4 shows that there is a tendency for colloid transport cases to result in thesame peak flux value as in the no-colloid case (normalised flux = 1.0). Only at highervalues of Kp than the reference case value do many of the points separate from thislevel, indicating that the presence of colloids causes higher radionuclide release fluxes(Figure 4.4 (a)). Similar comments apply to Figure 4.4 (b) at mα values above the

reference value for non-saline groundwater, where the separation from the normalisedflux = 1.0 starts at low values under the influence of high Kp.

As noted, Table 4.6 indicates that the radionuclide-colloid sorption coefficient, Kp,has the most influence on peak release of all of the individually sampled parameters.In Figure 4.4 (a), at the highest end of the reasonable range, the green diamond ataround 104 m3 kg-1 gives a flux which is around 5000 times higher than the peak fluxin the no-colloid case. Similarly, a slightly smaller Kp value gives a peak release overten thousand times higher. In addition to high Kp, these two runs also have fairly highvalues of the colloid load (αm) - more than a hundred times the non-saline colloid loadin the reference case.

Also of interest is the case that has Kp = 1.17×102 m3 kg-1 (17% higher than thereference case). For αm = 6.54×10-3 kg m-3 (350 times higher than the saline referencecase), the peak release is around fifty times higher than in the no-colloid case. For thisrun, the colloid sorption/desorption rate is near the critical value determined in Figure4.3 at 1.9×10-2.

Two points are singled out in Figure 4.4 (b), corresponding to values of colloid loadclose to the saline and non-saline reference values. They show values of peak releasearound a factor of 100 higher than the no-colloid case. Each corresponds to a run withvery high Kp values - respectively 9.7×104 and 1.8×104 m3 kg-1 - which are above thereasonable region. One of these runs has κ1 in the critical region identified in Figure4.3 (κ1 = 4×10-2 y-1). Thus, the results plotted in Figure 4.4 (b) suggest that for typicalSwedish groundwater colloid loads (αm), the radionuclide - colloid sorptioncoefficient, Kp, is effectively the only parameter that can significantly affect colloidtransport.

The sorption/desorption rate (κ1) is not indicated in Table 4.6 as being particularlyimportant in its influence on the timing and magnitude of release, despite the fact thatthe analysis reported in Sections 3.3 and 4.2 might suggest otherwise. This is becauseit has not been possible to extend the probabilistic analysis to times earlier than 100years, due to numerical difficulties in COLLAGE II at earlier times. In many modelcalculations, we have found that the peak release in the colloid case is earlier than inthe no-colloids case, and its magnitude is less than or similar to the peak with nocolloids. Had it been possible to run the probabilistic case from ten years, it is likelythat many of the peaks would have been before 100 years, and the effect of κ1 mayhave been more prominent. Individual runs were possible starting before this time andthese have been analysed separately below. The 100-year effective working limit isindicated in Figure 4.5 and Figure 4.6 by the shaded region, which denotes t < 100years.

37

In Figure 4.5 and Figure 4.6, the clustering of points around the same peak-flux valueas in the no-colloid case (approximately 3×105 years) indicates that the output timesrequested in the COLLAGE II runs were discretised. The true time of peak flux isprobably somewhere between the two bands of points indicated in the plots.

Results for some individual runs in the probabilistic sample set were able to yieldresults at early times <100 years. For example, one run (#30) had Kp = 5.4×103 m3 kgm-1, αm = 3×10−5 (mid-way between saline and non-saline cases) and κ1 = 2.6×10-3

y-1. These figures correspond to a reasonable colloid load and sorption/desorption ratein the critical region. The plot of release flux vs. time for this run is shown in Figure4.7. The run is of interest because it demonstrates an early colloid release flux (greenpoints) that is around two orders of magnitude higher than the solute flux. The valueof Kp is 54 times higher than the reference value from Degueldre (1994). While this isquite high, it is not unreasonable.

4.3.3 Key Parameter Sets

Our analyses have identified three key parameters that determine the likely impact ofradionuclide transport by colloids:

• Radionuclide-colloid sorption coefficient (Kp).• Suspended colloid load (αm).• Sorption/desorption rate (κ1).

Consideration of the results described above suggest that it may be useful to define arange of parameter sets relevant to colloid-facilitated transport in Swedish fractures.The sets are determined in terms of the three key parameters and are summarised inTable 4.7. Results illustrating the most pessimistic cases for radionuclide transport bycolloids are plotted in Figure 4.8.

The eight parameter sets distinguish themselves by variations in Kp (100 - 5000 m3

kg-1), in the groundwater colloid load associated with saline and non-saline conditions(respectively 2×10-5 and 4.5×10-5 kg m-3), and in the rate constant (κ1). Figure 4.8shows that for fast sorption/desorption (κ1 = 3.0 y-1), the peak flux is barely enhancedby a factor of two, with a slightly earlier peak. If, conversely, the kinetics are slow (κ1

= 0.08 y-1), there is the potential for a significantly higher release at times < 1,000years. The COLLAGE II code is not able to resolve the peak. However, a factor of 50(saline case) is possible, rising to over 100 in the non-saline case.

38

1x10 1 1x10 2 1x10 3 1x10 4 1x10 5 1x10 6 1x10 7

tim e [a ]

1x10 -9

1x10 -8

1x10 -7

1x10 -6

1x10 -5

1x10 -4

1x10 -3

rele

ase

flux

[m

ol m

-2 a

-1]

S am p le R u n 0030:K p = 5 .4×1 0 3 m 3 k g -1

αm = 3×1 0 -5 k g m -3

κ1 = 2 .6×1 0 -3 y -1

S o lu te f lu x

C o llo id flu x

S o lu te f lu x , n o co llo id s

lo w er lim it to o u tp u t in p ro b a b ilis tic sen sit iv ity a n a ly sis

Figure 4.7: Colloid and solute fluxes from sample run 30 compared to the case withno colloids. The combination of parameters represents colloid sorption,colloid load and colloid kinetics within a reasonable range. Enhancedtransport on colloids by up to two orders of magnitude is seen.

1x1 0 1 1x1 0 2 1x1 0 3 1x1 0 4 1x1 0 5 1x1 0 6 1x1 0 7

tim e [a ]

1x1 0 -1

1x1 0 0

1x1 0 1

1x1 0 2

1x1 0 3

flux

nor

mal

ised

to n

o co

lloid

pea

k

K B S critica l va lu es :K p = 5 .0×10 3 m 3 kg -1

n o co llo id s

sa lin e co n d itio n s, co llo id f lu x : κ1 = 0 .0 8 y -1

αm = 2 .0×1 0 -5 k g m -3

sa lin e co n d itio n s, so lu te f lu x :κ1 = 3 .0 y -1

αm = 2 .0×1 0 -5 k g m -3

n on -salin e con d itio ns , co llo id flu x :κ1 = 0 .0 8 y -1

αm = 4 .5×10 -5 k g m -3

n on -salin e con d itio ns , so lu te flux :κ1 = 3 .0 y -1

αm = 4 .5×10 -5 k g m -3

Figure 4.8: Identification of pessimistic case colloid transport parameters forgroundwater conditions and colloid populations defined by Swedish salineand non-saline groundwaters.

39

Table 4.7: Key parameters characterising plutonium transport in Swedish fractures inthe KBS-3 concept. Reference and early breakthrough cases.

Parameter Comments

Best estimate case - present-day groundwater conditions

Kp - colloid sorption coeff. 100 [m3 kg-1] Degueldre (1994)

αm - mobile colloid load 2×10-5 [kg m-3] Saline conditions (Laaksoharju et al., 1995)

κ1 - sorption/desorp. rate 3 [y-1] Interpretation of Lu et al. (2000)

Best estimate case - future non-saline groundwater conditions


αm - mobile colloid load 4.5×10-5 [kg m-3] Non-saline conditions (Laaksoharju et al., 1995)


Saline groundwater conditions - low sorption/desorption rate (BC3)


αm - mobile colloid load 2×10-5 [kg m-3] Non-saline conditions (Laaksoharju et al., 1995)

κ1 - sorption/desorp. rate 0.08 [y-1] Peak value, early release (Section 4.2.2)

Best estimate case - future non-saline groundwater conditions




High early release case - present-day groundwater conditions

Kp - colloid sorption coeff. 5000 [m3 kg-1] Section 4.3.2

αm - mobile colloid load 2×10-5 [kg m-3] Saline conditions (Laaksoharju et al., 1995)


High early release case - future non-saline groundwater conditions




High early release case - Saline groundwater conditions - low sorption/desorption rate


αm - mobile colloid load 2×10-5 [kg m-3] Non-saline conditions (Laaksoharju et al., 1995)


High early release case - Best estimate case - future non-saline groundwater conditions


αm - mobile colloid load 4.5×10-5 [kg m-3] Non-saline cond. (Laaksoharju et al., 1995)


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4.4 Other Radionuclides

Plutonium has been considered in the numerical assessment carried out here for anumber of reasons. First, it is an important component of the KBS-3 spent fuel sourceterm. Second, it is clearly associated with colloids at the NTS. Third, there is a usefulbody of knowledge relating to plutonium and its interaction with colloids. It istherefore sometimes used as a surrogate for the other actinides in the sense that manyof the properties are similar, and our aim is to establish significant areas of parameterspace where colloid-mediated effects might be seen.

SR97 (Lindgren and Lindström, 1999) indicates that plutonium and the actinides donot play a significant role in determining dose because they are not released to thebiosphere in sufficient quantities. Indeed, Lindgren and Lindström (1999) calculatedlittle release of plutonium from the near-field. The enhanced potential for the releaseof colloidal plutonium outlined here could certainly lead to higher doses from 242Pubut, to assess this properly, the release from the near-field in Figure 4.1 of Lindgrenand Lindström (1999) would need to be used as an input to the COLLAGE II code.

Other radionuclides are released from the near-field, including 226Ra, 237Np and 229Th.These nuclides have similar behaviour to plutonium. They all appear in the release atlate times but retardation in the far-field means that they do not play a significant rolein the determination of dose. The analysis performed in this study suggests that higherradionuclide-colloid sorption coefficients might lead to increased dose. The datagiven by Degueldre (1994) suggest that the actinides all have similar but uncertain Kp

values.

For groundwater colloid concentrations relevant to Swedish fractures, the Kp valuessuggested by Degueldre might lead to an early peak in the release flux whencombined with slow sorption/desorption rates. Lu et al. (2000) have considered thekinetics of a number of actinides in addition to Pu (Am, Np, and U) but theexperiments were all conducted over a timescale for which the critical range of κ1 isprobably not detectable. Enhanced transport of these radionuclides leading to releasefrom KBS-3 fractures at times comparable to the groundwater travel time cannot beruled out. The potential impact in PAs cannot be fully assessed without enhancementsto existing capabilities for representing colloids in PA.

The other radionuclides indicated as relevant in SR97 (Lindgren and Lindström,1999) are either anions (129I, 36Cl) or are otherwise not strongly sorbed to colloids(135Cs, 59Ni, 79Se - see Degueldre, 1994).

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5 Conclusions

The main objective of this project was to investigate the potential role of colloids inthe KBS-3 concept, taking account of recent developments in the study ofradionuclide transport by colloids.

The understanding of colloid transport and dynamics arising from a review of currentcolloid research activities in the US, combined with the analysis of the BENHAMobservations from the NTS, implies that colloids could play a more important rolethan previously recognised in the KBS-3 concept if similar processes operated.This is in contrast to earlier PA modelling in the context of radioactive wastemanagement (e.g., Nagra, 1994; Laaksoharju et al., 1995). The conditions underwhich significant transport might arise have been identified and the range ofparameters determined.

5.1 Modelling Plutonium Transport at the Nevada Test Site

Study of groundwater in the vicinity of the BENHAM test at the NTS has detected Puat a point 1.3 km downstream from the source. The Pu is currently associated withcolloids. Isotopic measurements have established that the Pu definitely came from theBENHAM test, which was conducted over 30 years ago. Plutonium is generally fairlyimmobile in groundwater systems, and it has been suggested that colloids may havecaused the plutonium to be transported 1.3 km in only 30 years. This hypothesis hasbeen tested by modelling plutonium transport in a fracture with similar characteristicsto those present in the vicinity of the BENHAM test.

Recently published data from both the ongoing NTS site investigation and from theYucca Mountain Project have been used to define a COLLAGE II dataset. Thekinetics of radionuclide-colloid sorption and desorption have been found to be crucialin explaining the transport of plutonium associated with colloids, as inferred at theNTS. Specifically, it has been found that for plutonium to have been transported bycolloids over the full 1.3-km transport path, it is likely that the plutonium was releasedin colloidal form and that the rate of plutonium desorption from colloids must havebeen slow.

The results obtained suggest that a programme of future monitoring observationswould be necessary in order to properly understand colloid transport associated withthe BENHAM test. If future observations at the NTS indicate a relatively short-livedpulse of Pu-bearing colloids, then it is likely that the Pu-bearing colloids weregenerated at the time of the nuclear explosion and that they have migrated throughfractures in the intervening years. If the fall-off in colloid concentration at theobservation wells is slow, and no peak is clearly resolved, our results imply that theplutonium on the colloids became attached during transport from the detonation point.

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On the balance of the available evidence, we consider that the most appropriateinterpretation of the BENHAM observations is that:

• Most of the plutonium inventory was released into the fracture on colloids.

• Plutonium - colloid interaction kinetics at the NTS proceeded at a rate less than0.1 y-1.

5.2 Colloids in Swedish PA

COLLAGE II has been used to evaluate the possible role of radionuclide transport bycolloids in the Swedish KBS-3 disposal concept. Sensitivity analyses using parametervalues relevant to Swedish fractures and groundwater hydrogeochemistry, combinedwith lessons from modelling the NTS observations, imply that colloid-facilitatedtransport of plutonium could be significant for the KBS-3 concept if:

1) Groundwater colloid concentrations are at or above observed levels.

2) Plutonium sorption to colloids is as strong as is currently estimated,

3) Pu - colloid sorption/desorption rates (κ1) are in a critical range from 0.02 to 0.2per year.

A combination of these factors could lead to releases of colloidal radionuclides atsimilar levels to releases estimated in previous PA studies, but at a much earlier time.

Early releases will only occur over a relatively restricted range of low Pu - colloidsorption/desorption rates. At these low rates, even if all plutonium is initially releasedin solution following diffusion through the bentonite buffer, a small amount is able toassociate with groundwater colloids. Because of the slow rate of disassociation, thisplutonium is then able to be carried significant distances on colloids before beingreleased to solution, where it is rapidly sorbed onto mineral surfaces.

The key to our results is the dynamic representation of radionuclide - colloidinteractions in COLLAGE II. Earlier performance assessments have not modelledthese interactions dynamically and so have not accounted explicitly for the kinetics ofradionuclide-colloid sorption.

We recommend, therefore, that a full PA-type calculation is made involving the 4N +i decay chains and including the near-field source term as input. This would help toassess the potential for colloid-facilitated transport to affect PA results.

On the basis of the COLLAGE II modelling carried out in this project, the relevantranges of key parameters likely to give rise to early releases of radionuclides bound tocolloids are:

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• Radionuclide - colloid sorption - Kp: 100 ≤ Kp ≤ 5000 m3 kg-1. Kp = 5000 m3 kg-1

is suitable for scoping calculations and is consistent with the values cited byDegueldre (1994).

• Colloid load in groundwater - αm: 2×10-5 ≤ αm ≤ 0.01 kg m-3.

• Radionuclide - colloid sorption/desorption rate - κ1: 0.02 ≤ κ1 ≤ 0.2 y-1.

A set of eight reference parameter sets have been suggested for future use in theassessment of the impact of colloid-facilitated transport in Swedish fractures.

Published data on present-day Swedish groundwater hydrogeochemistry, and colloidsorption kinetic data, suggest the following values: radionuclide - colloid sorptioncoefficient, Kp = 100 m3 kg-1, groundwater colloid load (saline conditions) αm =2×10-5 kg m-3, and plutonium - colloid sorption/desorption rate κ1 of the order 1 to 10y-1.

Modified colloid loads arising from an inflow of non-saline glacial meltwater mightresult in αm = 4.5×10-5 kg m-3, and our analysis indicates that at this value of αm, if thesorption/desorption rate is 0.08 y-1, then there is the potential for colloid-born releaseat early times.

Disposal concepts that do not employ bentonite may also give rise to significantlyhigher groundwater concentrations of colloids, because there is no bentonite to filterwaste- and repository-derived colloids. Moreover, in cementitious repositories,colloids may be generated as a result of the interaction of the near-field with the far-field. Higher concentrations of colloids may also occur for specific scenarios, such asearthquake or human intrusion scenarios involving breaching or degradation of thebentonite buffer. These are in most cases likely to be transient effects that will requirefurther investigation before their potential PA impact can be assessed.

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